Image Compression-JPEG Speaker: Ying Wun, Huang Adviser: Jian Jiun, Ding Date2011/10/14 1

Outline  Flowchart of JPEG (Joint Photographic Experts Group)  Correlation between pixels  Color space transformation-RGB to YCbCr & Downsampling  KL Transform & DCT Transform  Quantization  Zigzag Scan  Entropy Coding & Huffman Coding  MSE & PSNR  Conclusion  Reference 2

Flowchart of JPEG(Joint Photographic Experts Group) 3

Correlation between pixels  Correlation: HighLow  Compression ratio: HighLow Original Image 769KB Original Image 769KB Original Image 769KB Compressed Image 9KB Compressed Image 50KB Compressed Image 410KB 4

Color space transformation-RGB to YCbCr & Downsampling 5

 4:4:4 (No downsampling)  4:2:2 (Downsampling every 2 pixels in vertical or horizontal direction.)  4:2:0(Downsampling every 2 pixels in both vertical and horizontal direction.) 6 Color space transformation-RGB to YCbCr & Downsampling Y CbCb CrCr Y Y CbCb CrCr or YCbCb CrCr CbCb CrCr

KL Transform & DCT Transform  Fourier Transform & Fourier Series (1-Dimension): A signal can be expressed as a combination of sines and cosines.  KL Transform & DCT Transform (2-Dimension): A complex pattern can be expressed as a combination of many kinds of simple pattern (i.e. bases). 7

 Karhunen-Loeve Transform (KLT): Every image has its own bases (i.e. different image has different bases), we need to find and save the bases information during the process of compression.  Advantage: Minimums the Mean Square Error(MSE).  Disadvantage: Computationally expensive.  Discrete Cosine Transform (DCT): Compress different image by the same bases.  Advantage: Computationally efficient.  Disadvantage: The performance of MSE is not as well as KL Transform, but it’s good enough. 8 KLT & DCT 8x8 DCT bases

9 KLT & DCT

 Example of DCT: 10 KLT & DCT -76, -73, -67, -62, -58, -67, -64, -55, -65, -69, -73, -38, -19, -43, -59, -56, -66, -69, -60, -15, 16, -24, -62, -55, -65, -70, -57, -6, 26, -22, -58, -59, -61, -67, -60, -24, -2, -40, -60, -58, -49, -63, -68, -58, -51, -60, -70, -53, -43, -57, -64, -69, -73, -67, -63, -45, -41, -49, -59, -60, -63, -52, -50, -34 Before DCT: After DCT: , , , 27.24, 56.13, , -2.39, 0.46, 4.47, , , 10.25, 13.15, -7.09, -8.54, 4.88, , 7.37, 77.13, , , 9.93, 5.42, -5.65, , 12.07, 34.10, , , 6.30, 1.83, 1.95, 12.13, -6.55, , -3.95, -1.88, 1.75, -2.79, 3.14, -7.73, 2.91, 2.38, -5.94, -2.38, 0.94, 4.30, 1.85, -1.03, 0.18, 0.42, -2.42, -0.88, -3.02, 4.12, -0.66, -0.17, 0.14, -1.07, -4.19, -1.17, -0.10, 0.50, 1.68, , , , 27.24, 56.13, , -2.39, 0.46, 4.47, , , 10.25, 13.15, -7.09, -8.54, 4.88, , 7.37, 77.13, , , 9.93, 5.42, -5.65, , 12.07, 34.10, , , 6.30, 1.83, 1.95, 12.13, -6.55, , -3.95, -1.88, 1.75, -2.79, 3.14, -7.73, 2.91, 2.38, -5.94, -2.38, 0.94, 4.30, 1.85, -1.03, 0.18, 0.42, -2.42, -0.88, -3.02, 4.12, -0.66, -0.17, 0.14, -1.07, -4.19, -1.17, -0.10, 0.50, 1.68, AC terms: Small coefficient DC terms: Large coefficient

Quantization  We divide the DCT coefficients by Quantization Table to downgrade the value recorded in the jpeg file because it is hard for the human eyes to distinguish the strength of high frequency components.  Quantization Table: 11 Luminance quantization table Chrominance quantization table

 Example of Quantization: Before Quantization After Quantization 12 Quantization , , , 27.24, 56.13, , -2.39, 0.46, 4.47, , , 10.25, 13.15, -7.09, -8.54, 4.88, , 7.37, 77.13, , , 9.93, 5.42, -5.65, , 12.07, 34.10, , , 6.30, 1.83, 1.95, 12.13, -6.55, , -3.95, -1.88, 1.75, -2.79, 3.14, -7.73, 2.91, 2.38, -5.94, -2.38, 0.94, 4.30, 1.85, -1.03, 0.18, 0.42, -2.42, -0.88, -3.02, 4.12, -0.66, -0.17, 0.14, -1.07, -4.19, -1.17, -0.10, 0.50, 1.68, , , , 27.24, 56.13, , -2.39, 0.46, 4.47, , , 10.25, 13.15, -7.09, -8.54, 4.88, , 7.37, 77.13, , , 9.93, 5.42, -5.65, , 12.07, 34.10, , , 6.30, 1.83, 1.95, 12.13, -6.55, , -3.95, -1.88, 1.75, -2.79, 3.14, -7.73, 2.91, 2.38, -5.94, -2.38, 0.94, 4.30, 1.85, -1.03, 0.18, 0.42, -2.42, -0.88, -3.02, 4.12, -0.66, -0.17, 0.14, -1.07, -4.19, -1.17, -0.10, 0.50, 1.68, -26, -3, -6, 2, 2, -1, 0, 0, 0, -2, -4, 1, 1, 0, 0, 0, -3, 1, 5, -1, -1, 0, 0, 0, -3, 1, 2, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26, -3, -6, 2, 2, -1, 0, 0, 0, -2, -4, 1, 1, 0, 0, 0, -3, 1, 5, -1, -1, 0, 0, 0, -3, 1, 2, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, Quantize by lumunance quantization table We Get Many Zeros!

Zigzag Scan Zigzag Scan −26, −3, 0, −3, −3, −6, 2, −4, 1 −4, 1, 1, 5, 1, 2, −1, 1, −1, 2, 0, 0, 0, 0, 0, −1, −1, 0, ……,0. We get a sequence after the zigzag process: The remnants are Zeros! The sequence can be expressed as: (0:-26),(0:-3),(1:-3),…,(0:2),(5:-1),(0:-1),EOB Run-Length Encoding High Frequency Low Frequency

Entropy Coding & Huffman Coding  Key points: Encode the high/low probability symbols with short/long code length. 14 SymbolBinary Code …… DC luminance Huffman Table SymbolBinary Code RunSize 0100 ……… ……… ……… EOB1010 ZRL1111 AC luminance Huffman Table

MSE & PSNR 15

16 MSE & PSNR

 Blind spot of MSE & PSNR:  PSNR still looks fine even though we can easily find a obvious error on the right image, why?  It is due to the fact that PSNR is calculated from MSE, where MSE is the “MEAN” square error. 17 MSE & PSNR Correct Image PSNR = 30.4 Error Image PSNR = 32.6

Conclusion  As a conclusion, to compress a image, first we have to reduce the correlation between pixels, then quantize the image to reduce the high frequency components, finally encode the image by entropy coding to minimize code length to get a low data rate image. 18

Reference  [1] 酒井善則、吉田俊之 共著，白執善 編譯， 影像壓縮技術 映像 情報符号化，全華科技圖書股份有限公司, Oct  [2] WIKIPEDIA, “JPEG”,  [3] WIKIPEDIA, “PSNR”, 19

The End 20